Might the difference between Schrödinger and Ruedenberg's local contributions to the kinetic energy represent elastic deformations of the electron?

In Schrödinger's equation, the local contribution to the kinetic energy is sometimes negative, but it allows a conservative potential in contrast to an alternative, never negative, energy proposed by Ruedenberg. The total kinetic energy evaluated in certain characteristic volumes, and in all of space, is identical in the two cases. Dirac's suggestion in 1962 of a bubble-surface representing the electron is applied in a far-reaching, but incomplete, attempt to identify external kinetic energy with a first-order relativistic effect and the internal energy constituting the difference between Schrödinger and Ruedenberg's proposals is related to oscillations of the surface.     

Use of metastable peak shapes in determining ring size in cyclic rearrangements in the mass spectrometer

A general method is described in which the mechanism of a reaction occurring in the ion source is inferred from the kinetic energy release accompanying further fragmentation of metastable product ions. In several cases the probe reaction occurred competitively by two mechanisms, and if high energy resolution is available this allows the detailed metastable peak shapes and not merely the average kinetic energy released, to be used to characterize the product ion formed in the fast (ion source) reaction. It is found that most substituted benzaldoxime O-methyl ethers undergo HCN elimination via a five-centered methoxyl transfer in the ion source, but that the p-methoxy substituted compound reacts through both a four- and a five-membered cyclic intermediate. The slow reactions of the corresponding metastable ions occur predominantly through a four-centered transition state in the p-methoxy compound and probably through both four- and five-membered intermediates for the less strongly electron donating substituents. The fraction of the excess energy of the products is higher than expected from a consideration of energy partitioning data for other systems involving activated complexes of comparable tightness.     

On the lattice stability of metals

A tight-binding calculation for body-centred cubic (bcc) and face-centred cubic (fcc) lithium is carried out using muffin-tin potentials which differ only in the arrangement of the muffin-tin spheres. The essential results are not restricted to lithium but also hold for other metals with similar s-p-bands. The bcc structure can be stable for the lowest valence states. The stability of fcc increases with increasing valence electron concentration. This is due to the kinetic energy which behaves as in an empty lattice case. In accordance with the behaviour of the kinetic energy, the lowest energy states have the highest distribution probability between neighbouring atoms. They are mostly delocalized. The trend in the lattice stability is explained in terms of the differences in the packing of the lattices. In real cases where the virial theorem holds an appropriate part of the kinetic energy is changed into potential energy. Hybridization plays a completely different role from that in covalent compounds. It stabilizes a compound by delocalizing the charge density.     

Mapping the ion kinetic energy in a helium microwave plasma orthogonal acceleration time-of-flight mass spectrometer.

The ion kinetic energy of a helium microwave plasma is studied using an orthogonal acceleration time-of-flight mass spectrometer. The ions produced in the plasma are extracted into the mass spectrometer in an 'off-cone' mode (i.e. the helium plasma plume is off the sampler cone), and enter the repelling zone in the x-direction, which is perpendicular to the flight tube. The information of ion initial kinetic energy was obtained from both theoretical calculations and experimental results. The potential influence of two x-direction steering plates (X-steering plates) on the ion energy and signal intensity was examined. The influence of gas composition on the ion kinetic energy was also investigated. The calculated results show that ions with different m/z have different velocity and kinetic energy when they enter the ion modulation zone, and lighter ions have higher velocity and lower kinetic energy. The experimental results obtained demonstrate that the ion signals of different m/z produced with an 'off-cone' sampling helium microwave plasma show similar trends as calculated with the potential difference of the X-steering plates, revealing their narrow kinetic energy distribution in the x-direction. Under typical operating conditions, the x-direction kinetic energy of ions detected mostly range from about 14.9 eV for (7)Li(+) to 16.8 eV for (208)Pb(+).     

Periodic boundary condition induced breakdown of the equipartition principle and other kinetic effects of finite sample size in classical hard-sphere molecular dynamics simulation

We examine consequences of the non-Boltzmann nature of probability distributions for one-particle kinetic energy, momentum, and velocity for finite systems of classical hard spheres with constant total energy and nonidentical masses. By comparing two cases, reflecting walls (NVE or microcanonical ensemble) and periodic boundaries (NVEPG or molecular dynamics ensemble), we describe three consequences of the center-of-mass constraint in periodic boundary conditions: the equipartition theorem no longer holds for unequal masses, the ratio of the average relative velocity to the average velocity is increased by a factor of [N/(N-1)]1/2, and the ratio of average collision energy to average kinetic energy is increased by a factor of N/(N-1). Simulations in one, two, and three dimensions confirm the analytic results for arbitrary dimension.     

Laplacian of the Hamiltonian Kinetic Energy Density as an Indicator of Binding and Weak Interactions

The kinetic energy is the center of a controversy between two opposite points of view about its role in the formation of a chemical bond. One school states that a lowering of the kinetic energy associated with electron delocalization is the key stabilization mechanism of covalent bonding. In contrast, the opposite school holds that a chemical bond is formed by a decrease in the potential energy due to a concentration of electron density within the binding region. In this work, a topographic analysis of the Hamiltonian Kinetic Energy Density (KED) and its laplacian is presented to gain more insight into the role of the kinetic energy within chemical interactions. This study is focused on atoms, diatomic and organic molecules, along with their dimers. In addition, it is shown that the laplacian of the Hamiltonian KED exhibits a shell structure in atoms and that their outermost shell merge when a molecule is formed. A covalent bond is characterized by a concentration of kinetic energy, potential energy and electron densities along the internuclear axis, whereas a charge-shift bond is characterized by a fusion of external concentration shells and a depletion in the bonding region. In the case of weak intermolecular interactions, the external shell of the molecules merge into each other resulting in an intermolecular surface comparable to that obtained by the Non-covalent interaction (NCI) analysis.     

Role of isoconversional methods in varying activation energies of solid-state kinetics: I. isothermal kinetic studies

Solid-state kinetics was developed from kinetic concepts for reactions in homogeneous phase systems, which has created considerable debate over issues such as variable activation energy. This behavior has been viewed by some as a violation of basic chemical kinetic principles. Variation in activation energy has been detected by isoconversional or ‘model-free’ calculation methods. The relationship between different calculation methods and the occurrence of variable activation energy was investigated in this work by employing model-fitting and isoconversional methods to analyze simulated isothermal data. In addition, these approaches were applied for sulfameter-dioxolane solvate desolvation data. We showed that variable activation energy is of two types—a true variation that results from the complex nature of the solid-state process and an artifactual one resulting from the use of some isoconversional methods.     

The elimination of carbon monoxide from molecular ions of phenol and other [C6H6O]+˙ isomers

Phenol and five acyclic isomeric compounds have been investigated using electron impact and field ionization techniques, mass analysed ion kinetic energy spectrometry and collision induced dissociation mass analysed ion kinetic energy spectrometry. The kinetic energy release data corresponding to the elimination of carbon monoxide from the molecular ions show that at least two structures of the reactant ion are involved. The electron impact and field ionization collision induced dissociation mass analysed ion kinetic energy spectra indicate that under electron impact conditions, the phenol ion partially isomerizes to another ion structure. An isomerization of about 40% to the structure of cis-2-hexen-4-yn-1-al is in good accordance with the spectral data.     

On the local representation of the electronic momentum operator in atomic systems

The local quantum theory is applied to the study of the momentum operator in atomic systems. Consequently, a quantum-based local momentum expression in terms of the single-electron density is determined. The limiting values of this function correctly obey two fundamental theorems: Kato's cusp condition and the Hoffmann-Ostenhof and Hoffmann-Ostenhof exponential decay. The local momentum also depicts the electron shell structure in atoms as given by its local maxima and inflection points. The integration of the electron density in a shell gives electron populations that are in agreement with the ones expected from the Periodic Table of the elements. The shell structure obtained is in agreement with the higher level of theory computations, which include the Kohn-Sham kinetic energy density. The average of the local kinetic energy associated with the local momentum is the Weizsacker kinetic energy. In conclusion, the local representation of the momentum operator provides relevant information about the electronic properties of the atom at any distance from the nucleus.     

Kinetic energy density study of some representative semilocal kinetic energy functionals

There is a number of explicit kinetic energy density functionals for noninteracting electron systems that are obtained in terms of the electron density and its derivatives. These semilocal functionals have been widely used in the literature. In this work, we present a comparative study of the kinetic energy density of these semilocal functionals, stressing the importance of the local behavior to assess the quality of the functionals. We propose a quality factor that measures the local differences between the usual orbital-based kinetic energy density distributions and the approximated ones, allowing us to ensure if the good results obtained for the total kinetic energies with these semilocal functionals are due to their correct local performance or to error cancellations. We have also included contributions coming from the Laplacian of the electron density to work with an infinite set of kinetic energy densities. For all but one of the functionals, we have found that their success in the evaluation of the total kinetic energy is due to global error cancellations, whereas the local behavior of their kinetic energy density becomes worse than that corresponding to the Thomas-Fermi functional.     

Two-color visible/vacuum ultraviolet photoelectron imaging dynamics of Br2

An experimental two-color photoionization dynamics study of laser-excited Br2 molecules is presented, combining pulsed visible laser excitation and tunable vacuum ultraviolet (VUV) synchrotron radiation with photoelectron imaging. The X 1Sigmag + -B 3Pi0+u transition in Br2 is excited at 527 nm corresponding predominantly to excitation of the v' = 28 vibrational level in the B 3Pi0+u state. Tunable VUV undulator radiation in the energy range of 8.40-10.15 eV is subsequently used to ionize the excited molecules to the X 2Pi32,12 state of the ion, and the ionic ground state is probed by photoelectron imaging. Similar experiments are performed using single-photon synchrotron ionization in the photon energy range of 10.75-12.50 eV without any laser excitation. Photoelectron kinetic energy distributions are extracted from the photoelectron images. In the case of two-color photoionization using resonant excitation of the intermediate B 3Pi0+u state, a broad distribution of photoelectron kinetic energies is observed, and in some cases even a bimodal distribution, which depends on the VUV photon energy. In contrast, for single-photon ionization, a single nearly Gaussian-shaped distribution is observed, which shifts to higher energy with photon energy. Simulated spectra based on Franck-Condon factors for the transitions Br2(X 1Sigmag+, v" = 0)-Br2 +(X 2Pi12,32, v+) and Br2(B 3Pi0+u, v' = 28)-Br2 +(X 2Pi12,32, v+) are generated. Comparison of these calculated spectra with the measured images suggests that the differences in the kinetic energy distributions for the two ionization processes reflect the different extensions of the vibrational wave functions in the v" = 0 electronic ground state (X 1Sigmag+) versus the electronically and vibrationally excited state (B 3Pi0+u, v' = 28).     

Accuracy of enthalpy and entropy determination using the kinetic method: are we approaching a consensus?

There is an emerging consensus regarding the applicability of the kinetic method. All parties acknowledge that it is an approximate quantitative technique, capable of yielding not only enthalpy, but also entropy values. Opinions differ mainly on the accuracy of the results but it is agreed that the energy (effective temperature) dependence of kinetic method plots needs to be checked in all but the simplest of cases. When the 'apparent basicity' is found to depend on collision energy (and hence effective temperature), the extended kinetic method must be used. We have performed a large-scale modeling study, involving thousands of randomly selected molecular systems and a variety of experimental conditions, using exact calculations and realistic data sets. The results show that when the measured entropy difference between the two competing reaction channels is less than approximately 35 J mol(-1) K(-1), overall errors (standard deviations) of DeltaH(298) determined by the kinetic method are +/-5 kJ mol(-1); those of DeltaS(298) are +/-10 J mol(-1) K(-1). These include not only inherent errors of the kinetic method, but also errors in ion abundance measurement (5%) and inaccurate knowledge of reference compound thermochemistry (+/-2 kJ mol(-1), on average). We recommend, in general, that these errors be reported in kinetic method studies. When the measured entropy difference between the two competing fragmentation channels is large (>35 J mol(-1) K(-1)), it is likely to be significantly underestimated and errors of the kinetic method increase significantly.     

Translational spectroscopy of HNCO photodissociation

The kinetic energy released in the photodissociation of HNCO is measured by photofragment translational spectroscopy. In this study, CO is ionized by laser ionization immediately following its ejection from HNCO. The time for the CO ions to travel the length of our spectrometer is then measured, and the kinetic energy released by the photodissociation is calculated. Changing the wavelength of the laser that ionizes the CO changes the selected internal energy and the expected change in the kinetic energy release is observed. These data confirm that the threshold for NH (a ¹Δ) production is the dissociation energy.     

Application of the golden section search algorithm in the nonlinear isoconversional calculations to the determination of the activation energy from nonisothermal kinetic conversion data

In this study, the golden section search algorithm in the nonlinear isoconversional calculations to be used for the determination of the activation energy from nonisothermal kinetic conversion data has been introduced. The technique has been applied to two simulated processes (one corresponds to a constant activation energy process, and the other corresponds to a varying activation energy process) and cellulose pyrolysis. The results have shown that the golden section search algorithm is capable of providing the valid activation energy values.     

Kinetic energy release in ionic fragmentations: Use as an ion structure probe

The kinetic energy released in unimolecular reactions, as measured from the width of the corresponding metastable peak, shows only a small dependence on such parameters as source temperature, ion-source residence time and ion acceleration voltage. Similarly, fragmenting ions generated from different members of an homologous series of molecular ions have been found to release the same kinetic energy and hence do not exhibit a degrees-of-freedom effect analogous to that for metastable abundances. In general, molecular ions formed by electron-impact have been found to release slightly less kinetic energy on fragmentation than the corresponding ions formed via a fragmentation sequence. These observations suggest that kinetic energy release is a useful method of structural characterization of metastable ions; while increase in the average internal energies of the ions sample lead to larger energy releases, this effect is usually small. The use of a very narrow energy resolving (β) slit and a procedure in which the metastable peak width is extrapolated to zero slit width has been found to improve the accuracy of measurement of the kinetic energy release, particularly when the metastable and main beam peak widths are of comparable magnitude.     

Failure of the Weizs?cker kinetic energy functional for one-, two-, and three-electron distribution functions

Further progress in pair-density functional theory (sometimes called 2-DFT) hinges on the development of computationally facile and quantitatively accurate models for the kinetic energy functional. In this paper we perform computational tests for two of the simplest models, the generalized Weizs?cker kinetic energy functional and its spin-resolved extension. Both of these models perform very poorly for atoms. The higher-order Weizs?cker functionals (based on the three-electron distribution function) perform better, but are still not successful. This suggests that an alternative approach for designing kinetic energy functionals of the pair density is needed.     

Ground and excited state dissociation dynamics of ionized 1,1-difluoroethene

The kinetic energy release distributions (KERDs) for the fluorine atom loss from the 1,1-difluoroethene cation have been recorded with two spectrometers in two different energy ranges. A first experiment uses dissociative photoionization with the He(I) and Ne(I) resonance lines, providing the ions with a broad internal energy range, up to 7 eV above the dissociation threshold. The second experiment samples the metastable range, and the average ion internal energy is limited to about 0.2 eV above the threshold. In both energy domains, KERDs are found to be bimodal. Each component has been analyzed by the maximum entropy method. The narrow, low kinetic energy components display for both experiments the characteristics of a statistical, simple bond cleavage reaction: constraint equal to the square root of the fragment kinetic energy and ergodicity index higher than 90%. Furthermore, this component is satisfactorily accounted for in the metastable time scale by the orbiting transition state theory. Potential energy surfaces corresponding to the five lowest electronic states of the dissociating 1,1-C2H2F2+ ion have been investigated by ab initio calculations at various levels. The equilibrium geometry of these states, their dissociation energies, and their vibrational wavenumbers have been calculated, and a few conical intersections between these surfaces have been identified. It comes out that the ionic ground state X2B1 is adiabatically correlated with the lowest dissociation asymptote. Its potential energy curve increases in a monotonic way along the reaction coordinate, giving rise to the narrow KERD component. Two states embedded in the third photoelectron band (B2A1 at 15.95 eV and C2B2 at 16.17 eV) also correlate with the lowest asymptote at 14.24 eV. We suggest that their repulsive behavior along the reaction coordinate be responsible for the KERD high kinetic energy contribution.     

一些双电荷离子的气相碎裂反应

借助质量分析离子动能谱和串联质谱研究了由电子轰击产生的双电荷离子的单分子亚稳碎裂及碰撞诱导分解过程,讨论了两种实验方法导致的差别因素.此外,根据质量分析离子动能谱提供的双电荷离子电荷分离反应的动能释放值计算了两电荷中心间距的最小值,以判别按不同电荷分离方式碎裂的双电荷离子的过渡态结构.     

N2+2离子在线偏振和圆偏振强激光场中的解离

基于N+离子的飞行时间质谱, 研究了N2+2离子在线偏振和圆偏振强飞秒激光场中(45 fs, 5×1015-1×1016 W·cm-2, 800 nm)的解离. 通过对N+离子质谱和平动能的分析发现, N2+2离子在线偏振光和圆偏振光作用下具有不同的解离方式. 在线偏振光下, N2分子在平衡核间距RE处发生次序双电离生成N2+2离子, N2+2离子解离所释放的能量能够用单光子跃迁模型来解释. 而在圆偏振光下, N2分子首先电离生成N+2离子, N+2离子在核间距增大到临界核间距RC(>RE)时, 进一步被电离从而发生解离, 此时解离所释放的能量可以用库仑推斥模型来解释.     

载能碳离子撞击石墨烯中Stone-Wales缺陷的动力学研究

采用分子动力学模拟方法,研究了载能碳离子撞击石墨烯中Stone-Wales缺陷的动力学过程,计算了Stone-Wales缺陷中初级碰撞原子的离位阈能和载能碳离子使其移位的入射阈能,并与完美石墨烯结构计算结果进行对比。通过分析初级碰撞原子与入射离子动能和势能随时间的变化关系,研究了碰撞过程中能量转移过程。研究结果表明,初级碰撞原子产生离位并最终脱离石墨烯体系的最小能量为25.0 eV。当初始动能为23.0 eV时,Stone-Wales缺陷中2个七元环共用的碳-碳键旋转90°形成了完美的石墨烯结构。此外,还发现使Stone-Wales缺陷中初级碰撞原子发生离位的载能碳离子最小入射能为41.0 eV。